Hamiltonian Variational Auto-Encoder

Variational Auto-Encoders (VAEs) have become very popular techniques to perform inference and learning in latent variable models as they allow us to leverage the rich representational power of neural networks to obtain flexible approximations of the posterior of latent variables as well as tight evidence lower bounds (ELBOs). Combined with stochastic variational inference, this provides a methodology scaling to large datasets. However, for this methodology to be practically efficient, it is necessary to obtain low-variance unbiased estimators of the ELBO and its gradients with respect to the parameters of interest. While the use of Markov chain Monte Carlo (MCMC) techniques such as Hamiltonian Monte Carlo (HMC) has been previously suggested to achieve this [23, 26], the proposed methods require specifying reverse kernels which have a large impact on performance. Additionally, the resulting unbiased estimator of the ELBO for most MCMC kernels is typically not amenable to the reparameterization trick. We show here how to optimally select reverse kernels in this setting and, by building upon Hamiltonian Importance Sampling (HIS) [17], we obtain a scheme that provides low-variance unbiased estimators of the ELBO and its gradients using the reparameterization trick. This allows us to develop a Hamiltonian Variational Auto-Encoder (HVAE). This method can be reinterpreted as a target-informed normalizing flow [20] which, within our context, only requires a few evaluations of the gradient of the sampled likelihood and trivial Jacobian calculations at each iteration.Comment: Accepted as a poster in the proceedings of the 32nd Conference on Neural Information Processing Systems (NeurIPS

Relating Regularization and Generalization through the Intrinsic Dimension of Activations

Given a pair of models with similar training set performance, it is natural to assume that the model that possesses simpler internal representations would exhibit better generalization. In this work, we provide empirical evidence for this intuition through an analysis of the intrinsic dimension (ID) of model activations, which can be thought of as the minimal number of factors of variation in the model's representation of the data. First, we show that common regularization techniques uniformly decrease the last-layer ID (LLID) of validation set activations for image classification models and show how this strongly affects generalization performance. We also investigate how excessive regularization decreases a model's ability to extract features from data in earlier layers, leading to a negative effect on validation accuracy even while LLID continues to decrease and training accuracy remains near-perfect. Finally, we examine the LLID over the course of training of models that exhibit grokking. We observe that well after training accuracy saturates, when models ``grok'' and validation accuracy suddenly improves from random to perfect, there is a co-occurent sudden drop in LLID, thus providing more insight into the dynamics of sudden generalization.Comment: NeurIPS 2022 OPT and HITY workshop

CaloMan: Fast generation of calorimeter showers with density estimation on learned manifolds

Precision measurements and new physics searches at the Large Hadron Collider require efficient simulations of particle propagation and interactions within the detectors. The most computationally expensive simulations involve calorimeter showers. Advances in deep generative modelling - particularly in the realm of high-dimensional data - have opened the possibility of generating realistic calorimeter showers orders of magnitude more quickly than physics-based simulation. However, the high-dimensional representation of showers belies the relative simplicity and structure of the underlying physical laws. This phenomenon is yet another example of the manifold hypothesis from machine learning, which states that high-dimensional data is supported on low-dimensional manifolds. We thus propose modelling calorimeter showers first by learning their manifold structure, and then estimating the density of data across this manifold. Learning manifold structure reduces the dimensionality of the data, which enables fast training and generation when compared with competing methods.Comment: Accepted to the Machine Learning and the Physical Sciences Workshop at NeurIPS 202

Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models

We systematically study a wide variety of generative models spanning semantically-diverse image datasets to understand and improve the feature extractors and metrics used to evaluate them. Using best practices in psychophysics, we measure human perception of image realism for generated samples by conducting the largest experiment evaluating generative models to date, and find that no existing metric strongly correlates with human evaluations. Comparing to 17 modern metrics for evaluating the overall performance, fidelity, diversity, rarity, and memorization of generative models, we find that the state-of-the-art perceptual realism of diffusion models as judged by humans is not reflected in commonly reported metrics such as FID. This discrepancy is not explained by diversity in generated samples, though one cause is over-reliance on Inception-V3. We address these flaws through a study of alternative self-supervised feature extractors, find that the semantic information encoded by individual networks strongly depends on their training procedure, and show that DINOv2-ViT-L/14 allows for much richer evaluation of generative models. Next, we investigate data memorization, and find that generative models do memorize training examples on simple, smaller datasets like CIFAR10, but not necessarily on more complex datasets like ImageNet. However, our experiments show that current metrics do not properly detect memorization: none in the literature is able to separate memorization from other phenomena such as underfitting or mode shrinkage. To facilitate further development of generative models and their evaluation we release all generated image datasets, human evaluation data, and a modular library to compute 17 common metrics for 9 different encoders at https://github.com/layer6ai-labs/dgm-eval.Comment: NeurIPS 2023. 53 pages, 29 figures, 12 tables. Code at https://github.com/layer6ai-labs/dgm-eval, reviews at https://openreview.net/forum?id=08zf7kTOo

The Union of Manifolds Hypothesis and its Implications for Deep Generative Modelling

Deep learning has had tremendous success at learning low-dimensional representations of high-dimensional data. This success would be impossible if there was no hidden low-dimensional structure in data of interest; this existence is posited by the manifold hypothesis, which states that the data lies on an unknown manifold of low intrinsic dimension. In this paper, we argue that this hypothesis does not properly capture the low-dimensional structure typically present in data. Assuming the data lies on a single manifold implies intrinsic dimension is identical across the entire data space, and does not allow for subregions of this space to have a different number of factors of variation. To address this deficiency, we put forth the union of manifolds hypothesis, which accommodates the existence of non-constant intrinsic dimensions. We empirically verify this hypothesis on commonly-used image datasets, finding that indeed, intrinsic dimension should be allowed to vary. We also show that classes with higher intrinsic dimensions are harder to classify, and how this insight can be used to improve classification accuracy. We then turn our attention to the impact of this hypothesis in the context of deep generative models (DGMs). Most current DGMs struggle to model datasets with several connected components and/or varying intrinsic dimensions. To tackle these shortcomings, we propose clustered DGMs, where we first cluster the data and then train a DGM on each cluster. We show that clustered DGMs can model multiple connected components with different intrinsic dimensions, and empirically outperform their non-clustered counterparts without increasing computational requirements

Edoxaban versus warfarin in patients with atrial fibrillation

Contains fulltext : 125374.pdf (publisher's version ) (Open Access)BACKGROUND: Edoxaban is a direct oral factor Xa inhibitor with proven antithrombotic effects. The long-term efficacy and safety of edoxaban as compared with warfarin in patients with atrial fibrillation is not known. METHODS: We conducted a randomized, double-blind, double-dummy trial comparing two once-daily regimens of edoxaban with warfarin in 21,105 patients with moderate-to-high-risk atrial fibrillation (median follow-up, 2.8 years). The primary efficacy end point was stroke or systemic embolism. Each edoxaban regimen was tested for noninferiority to warfarin during the treatment period. The principal safety end point was major bleeding. RESULTS: The annualized rate of the primary end point during treatment was 1.50% with warfarin (median time in the therapeutic range, 68.4%), as compared with 1.18% with high-dose edoxaban (hazard ratio, 0.79; 97.5% confidence interval [CI], 0.63 to 0.99; P<0.001 for noninferiority) and 1.61% with low-dose edoxaban (hazard ratio, 1.07; 97.5% CI, 0.87 to 1.31; P=0.005 for noninferiority). In the intention-to-treat analysis, there was a trend favoring high-dose edoxaban versus warfarin (hazard ratio, 0.87; 97.5% CI, 0.73 to 1.04; P=0.08) and an unfavorable trend with low-dose edoxaban versus warfarin (hazard ratio, 1.13; 97.5% CI, 0.96 to 1.34; P=0.10). The annualized rate of major bleeding was 3.43% with warfarin versus 2.75% with high-dose edoxaban (hazard ratio, 0.80; 95% CI, 0.71 to 0.91; P<0.001) and 1.61% with low-dose edoxaban (hazard ratio, 0.47; 95% CI, 0.41 to 0.55; P<0.001). The corresponding annualized rates of death from cardiovascular causes were 3.17% versus 2.74% (hazard ratio, 0.86; 95% CI, 0.77 to 0.97; P=0.01), and 2.71% (hazard ratio, 0.85; 95% CI, 0.76 to 0.96; P=0.008), and the corresponding rates of the key secondary end point (a composite of stroke, systemic embolism, or death from cardiovascular causes) were 4.43% versus 3.85% (hazard ratio, 0.87; 95% CI, 0.78 to 0.96; P=0.005), and 4.23% (hazard ratio, 0.95; 95% CI, 0.86 to 1.05; P=0.32). CONCLUSIONS: Both once-daily regimens of edoxaban were noninferior to warfarin with respect to the prevention of stroke or systemic embolism and were associated with significantly lower rates of bleeding and death from cardiovascular causes. (Funded by Daiichi Sankyo Pharma Development; ENGAGE AF-TIMI 48 ClinicalTrials.gov number, NCT00781391.)